I would say you might burn a few more calories when exercising in the cold (room or outside), but not enough to make a difference. That's only my guess, however. We get pretty cold winters up here, but I sure don't lose any more weight as compared to the other seasons.

I would place it in the same category as exercising in sweats, so that you sweat more. Just because you sweat out more fluid doesn't mean you are burning more calories.

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Northern Belle
Do or don't do; there is no try (Yoda)

I don't think so your heart rate tends to get higher faster in the heat- which is usually more indicative of calories burn.
You may burn a couple of more calories each day in cold weather just by your body having to work a bit more to stay at 97 degrees.

The first thing I thought of when I read this post was our bodies' natural tendency to put on an extra layer of fat in cold weather. I don't know if you would burn more calories in the cold or not, but I do Know our natural tendency is not to be thinner in cold weather.